Recently metamaterials have been demonstrating new physics to enable various unprecedented electromagnetic properties, but pratically they are so sensitive to incident angles of the external excitation that their applications are restricted. Therefore, we present an anisotropic negative refractive index medium operated at multiple-angle incidences (NRIM for MAI) to ease such a burden. Both the simulated and measured transmittance, reflectance and the corresponding material parameters indicate that our structure does possess the anisotropic negative refractive index with respect to different incident angles. In addition, the opposite directions of group and phase velocities are also demonstrated under both grazing-angle, normal and 45-degree incidences to further verify the negative refractive index of the designed monolithic NRIM structure for multiple-angle incidences.